On the syntactic analysis of figures

Many investigators have made use of syntactic analysis of figures for pattern recognition purposes during the recent years. Also a general theory of pattern analysis has been formulated recently be Grenander. Most of the earlier investigators concentrated their attention on the problem of line patterns, namely figures which could be composed by thin lines. Such is the case, for example, of the bubble chamber photographs. This paper attempts to develop a similar analysis for the case of set patterns and in particular for polygons. Any two-dimensional figure could be reduced into this form by quantizing its levels of illumination. Then all points with a given level of illumination form a plane set. Such sets could then be approximated by polygons. This could be achieved by a computer-controlled scanner with rectilinear motion or by a number of other techniques. Sometimes the polygonal approximation is only implicit (see the section on Implementation, below). The reason for the polygonal approximation will become evident in the next section. It should be emphasized that this process and the subsequent analysis which is the subject of this paper, are very sensitive to noise, and therefore, a prefiltering of the figure may be necessary. This sensitivity is a common feature of all the techniques which deal with the analysis of figures in simpler components. A more detailed discussion of these points is given elsewhere. In this paper we will try to emphasize only the basic ideas of our approach.